Real Numbers

Real numbers are the numbers that are either rational or irrational, i.e., the set of real numbers is the union of the sets Q and H. If the set of real numbers is denoted by R , then

R = Q È H

Since Q and H are mutually exclusive sets, any member of R is also a member of only one of the sets Q and H. Therefore, a real number is either rational or irrational (but not both). If a real number is rational, it can be expressed as an integer, as the quotient of two integers, and it can be represented by a terminating or repeating decimal; otherwise, it is irrational and cannot be represented in the above formats.